Absolute Value Equations & Inequalities

A carpenter is cutting boards for a shelving unit. Each board is supposed to be 85 centimeters long, but the length is allowed to differ from that by at most 0.2 cm. Write an absolute-value to represent the board lengths that would be unacceptable.

The drama club set a goal for each member to sell 20 tickets to their play. The students with the highest and lowest actual sales were exactly 11 tickets from this goal. Write an absolute-value to represent both the highest and lowest number of tickets sold by an individual.

The owner of a butcher shop keeps the freezer at −5 °C. It is acceptable for the temperature to be above or below this by as much as 1.5 °C. Write an absolute-value to represent the range of acceptable temperatures for the freezer.

Lucia sets the thermostat in the apartment to 68 degrees. The actual temperature in the apartment can vary from this by as much as 3 degrees. Write an absolute- value to represent the lowest and highest temperatures that occur in the apartment.

Rani is selling her car, which gets around 24 mpg (miles per gallon). However, her gas mileage varies from this by up to (but not including) 6 miles per gallon depending on where and how she drives. Write an absolute-value to represent the range of her car's gas mileage.

At Klondike Trout Farm, most of the trout have a length of 9.25 inches. The length of some of the trout differs from this by no more than 0.75 inches. Write an absolute-value to represent the range of lengths of the trout.

According to the World Health Organization, water temperatures ranging from 78 to 86 degrees Fahrenheit (inclusive) are generally comfortable and safe for those exercising in a swimming pool. Write an absolute-value to represent this range of temperatures.

https://apps.who.int/iris/handle/10665/43336

Though there are many factors that affect student achievement, a commonly discussed factor is class size. In 2020, the average class size in United States high schools ranged from 29 students (Utah) down to 17 students (Maine). Write an absolute-value to represent the range of average class sizes that year.

With an average of 25 students per class, Minnesota ranked sixth highest.

https://www.zippia.com/advice/states-most-crowded-schools-largest-classes/

A pedestrian bridge is 53 meters long. Due to changes in temperature, the bridge may expand or contract by as much as 21 millimeters. Write an absolute-value to represent the minimum and maximum lengths of the bridge.

Write an absolute-value to represent the recommended minimum and maximum daily intakes of iron.

A jewelry maker cuts pieces of wire to shape into earrings. The equation $$\left|x-18\right|=1.1$$  gives the minimum and maximum lengths in centimeters of the wires used for various designs. Calculate the shortest length of wire used.